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Evidence on the Speed of Convergence to Market Efficiency by Tarun Chordia, Richard Roll, and Avanidhar Subrahmanyam April 11, 2004

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Evidence on the Speed of Convergence to Market Efficiency by Tarun Chordia, Richard Roll, and Avanidhar Subrahmanyam April 11, 2004 Evidence on the Speed of Convergence to Market Efficiency by Tarun Chordia, Richard Roll, and Avanidhar Subrahmanyam April 11, 2004 Abstract Daily returns for stocks listed on the New York Exchange (NYSE) are not serially dependent. In contrast, order imbalances on the same stocks are highly persistent from day to day. These two empirical facts can be reconciled if sophisticated investors react to order imbalances within the trading day by engaging in countervailing trades sufficient to remove serial dependence over the daily horizon. How long does this actually take? The pattern of intra-day serial dependence, over intervals ranging from five minutes to one hour, reveals traces of efficiency-creating actions. For the actively-traded NYSE stocks in our sample, it takes longer than five minutes for astute investors to begin such activities. By thirty minutes, they are well along on their daily quest. Contacts Chordia Roll Subrahmanyam Voice: 1-404-727-1620 1-310-825-6118 1-310-825-5355 Fax: 1-404-727-5238 1-310-206-8404 1-310-206-5455 E-mail: [email protected] [email protected] [email protected] Address: Goizueta Business School Anderson School Anderson School Emory University UCLA UCLA Atlanta, GA 30322 Los Angeles, CA 90095-1481 Los Angeles, CA 90095-1481 We are grateful to Michael Brennan, Jeff Busse, Eugene Fama, Laura Frieder, Will Goetzmann, Clifton Green, Andrew Karolyi, Pete Kyle, Francis Longstaff, Steve Ross, Ross Valkanov, Kumar Venkatraman, Ingrid Werner, and seminar participants at Bocconi University, Princeton University, Southern Methodist University, Texas A&M University, the New York Stock Exchange, the 2002 Western Finance Association Conference, and the 2002 University of Maryland Finance Conference for valuable comments and suggestions. We also appreciate financial support in the form of a grant from the Q-Group. Evidence on the Speed of Convergence to Market Efficiency Abstract Daily returns for stocks listed on the New York Exchange (NYSE) are not serially dependent. In contrast, order imbalances on the same stocks are highly persistent from day to day. These two empirical facts can be reconciled if sophisticated investors react to order imbalances within the trading day by engaging in countervailing trades sufficient to remove serial dependence over the daily horizon. How long does this actually take? The pattern of intra-day serial dependence, over intervals ranging from five minutes to one hour, reveals traces of efficiency-creating actions. For the actively-traded NYSE stocks in our sample, it takes longer than five minutes for astute investors to begin such activities. By thirty minutes, they are well along on their daily quest. 2 Convergence to Efficiency, April 11, 2004 Evidence on the Speed of Convergence to Market Efficiency Introduction For most of its scientific life, the field of finance has debated the question of market efficiency. Despite a long list of empirical anomalies and extensive indications of psychological quirks among investors, most financial economists and professionals still profess that asset prices are difficult to predict. Schwert (2001) reviews a number of well-documented anomalies and finds that some of them have disappeared, perhaps revealing ephemeral market inefficiencies. But he argues also that other anomalies appear to have been “discovered” even though they did not exist. There is a growing literature about the irrationalities of individual investors. Odean (1999), for instance, finds that small investors have a perverse ability to forecast future returns; their stock purchases perform worse than their sales. Barber and Odean (2000) find that the more individuals trade, the worse their returns. Benartzi and Thaler (2001) document bizarre portfolio choices among individuals allocating pension assets to various classes. Despite their reluctance to forecast prices, most scholars admit also that some individuals behave foolishly all the time and all individuals behave foolishly some of the time. When reconciling these conflicting views, we usually resort to flurry of hand waving and invoke the mantra of aggregation. Somehow, from within the blizzard of behavioral proclivities, the “market” becomes efficient, or, at least efficient enough that professors and money managers have a very Convergence to Efficiency, April 11, 2004 3 difficult time beating passive investment strategies. But exactly how does this happen and how long does it take? The concepts of market efficiency as defined by Fama (1970) in his seminal review, weak, semi- strong, or strong form efficiency, represent a road map for statistical tests. They offer little insight about market processes that might deliver the hypothesized phenomena. Clearly, efficiency does not just congeal from spontaneous combustion. It depends, somehow, on individual actions. This idea was formalized by Grossman (1976) and Grossman and Stiglitz (1980) who proved that the market price cannot fully incorporate all knowable information. Someone must be able to make (infra-marginal) returns from exploiting deviation of prices from fundamental values. But whom, and how? Cornell and Roll (1981) borrowed a model from evolutionary biology to show that efficient markets must be inhabited by both passive investors, who take prices as correct forecasts of future value, and by active investors who expend resources in an effort to detect errors in prices. Market efficiency is the state in which neither the marginal active nor the marginal passive investor has an incentive to alter his or her respective approach. Infra-marginal active investors pay to become better informed and somehow move prices enough that passive investors can enjoy a free ride without sacrificing much return (indeed, any return at the margin). Many investors still follow technical trading strategies that appear to generate little revenue and much cost; these strategies have long been the subject of much critique by finance professors. Recently, Chordia, Roll, and Subrahmanyam (2002) document a seemingly related and intriguing 4 Convergence to Efficiency, April 11, 2004 phenomenon during a study of market-wide order imbalances on the New York Stock Exchange. Market order imbalance, defined as the aggregated daily market purchase orders less sell orders for stocks in the S&P500 index, is highly predictable from day to day. A day with a high imbalance on the buy side will likely be followed by several additional days of aggregate buy side imbalance; and similarly for an imbalance on the sell side. This implies that investors continue buying or selling for quite a long time, either because they are herding or because they are splitting large orders across days, or both. More than fifty percent of tomorrow’s imbalance among S&P500 stocks can be forecast by past returns and past imbalances. Yet the S&P500 index is virtually a random walk over a horizon of one day. During the 1996- 2002 sample period, it had a first order autocorrelation coefficient of -0.0015 (p-value=0.95) and insignificant autocorrelations at all longer daily lags. This suggests, of course, that some astute investors must be correctly forecasting continuing price pressure from order imbalances and conducting countervailing trades within the very first day, trades sufficient to remove all serial dependence in returns, which would otherwise be induced by the continuing procession of order imbalances. There are at least two puzzles here: First, why do some naïve investors persist in their orders for days on end when it does them no good (because there is no inter-day return dependence)? Second, how long within the day does pressure from order imbalances continue to move prices? When thinking about this second and more important question, it seems rather obvious that some finite time period, albeit perhaps quite a short period, is required for sophisticated investors to counteract a sudden and unexpected preponderance of orders on the same side of the market. Convergence to Efficiency, April 11, 2004 5 It simply cannot be true that returns are independent from trade to trade or even from minute to minute. It must take at least some time for astute investors to figure out what is happening to orders, to ascertain whether there is new pertinent information about values, and to expunge any serial dependence remaining after prices adjust to their new equilibrium levels. The horizon over which this activity takes place is the object of our study. We propose to investigate how long it takes the market to achieve weak-form efficiency; i.e., how long it takes to remove return dependence. Other researchers have investigated questions similar to the one we address, but in very specific contexts. In early work, Patell and Wolfson (1984) show that dividend and earnings announcements “interrupt” the usual pattern of return serial dependence for at least fifteen minutes and that prices do not revert completely to their normal serial correlation pattern for up to ninety minutes. Although they make no explicit statement about how this happens, they clearly have in mind the activities of arbitrageurs who offset the impulsive reactions to company announcements of naïve investors. Garbade and Lieber (1977) formulate a model of independent changes in equilibrium price coupled with random orders to buy or to sell at quoted ask and bid prices. They use data on two stocks for a single month and find that this model does not describe price moves for short time intervals (a few minutes) while it is consistent with price moves over longer horizons.1 In 1 Unlike us, Garbade and Lieber (1977) do not have access bid-ask quote mid-points and hence are unable to separate bid-ask bounce in transaction prices from true serial correlation. 6 Convergence to Efficiency, April 11, 2004 concluding, they recognize that “…investors who monitor the market continually during the day…” might be instrumental in bringing about the observed pattern. Epps (1979) studies price adjustments for a group of firms in the same industry (automobiles).
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